micoeconomics hkust

Problem 3 (Production and Supply) Consider a firm with a production function q = f(K, L) = 3K1/312/3, who faces input prices w = 1 and v = 4. In the short run, the firm has a fixed amount of capital K = 27. (a) Find the long-run cost when q = 72. Explain why C(72) # SC(72). (b) Find the long-run cost when q = 156. Explain why C(156) # SC(156). (c) Graph the long-run and short-run total cost functions together, labeling specific values for C(72), C(156), SC(0), SC(72), and SC(156). Label the output where LTC(q) = STC(q) by q*. (d) Find the value of q*